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Byju's Answer
Standard VI
Mathematics
Construction of Perpendicular from a Point Outside the Line Using a Compass
Select the th...
Question

Select the third and fourth steps in the construction of a perpendicular to a line from a point outside the line using a ruler and compass.

A
Draw line MN and take any point K outside the line.
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B
Placing the compass point at point K and using any convenient distance, draw arcs to cut the line MN at two points A and B.
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C
Place the compass point at A and taking a distance greater than half of AB, draw an arc on the lower side of line MN.
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D
Place the compass point at B and using the same distance, draw an arc to cut the previous arc at T.
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Solution

The correct options are
C Place the compass point at A and taking a distance greater than half of AB, draw an arc on the lower side of line MN.
D Place the compass point at B and using the same distance, draw an arc to cut the previous arc at T.
Steps in the construction of a perpendicular to a line from a point outside the line using a ruler and compass are as follows:
  1. Draw line MN and take any point K outside the line.
  2. Placing the compass point at point K and using any convenient distance, draw arcs to cut the line MN at two points A and B.
  3. Place the compass point at A and taking a distance greater than half of AB, draw an arc on the lower side of line MN.
  4. Place the compass point at B and using the same distance, draw an arc to cut the previous arc at T.
  5. Draw the line KT.
Line KT is perpendicular to line MN.

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Q. Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw a line MN perpendicular to line AB.
Q. Arrange the steps of construction of a perpendicular to a line at a point on the line using a compass in correct order:
(A). Draw line MN and take point K anywhere on the line.
(B). Place the compass point at A and, taking a convenient distance greater than half the length of AB, draw AN ARC on one side of the line.
(C). Place the compass point on point K. Draw TWO ARCS on either side of point K to cut the line MN at equal distances from K. Name the points of intersection A and B respectively.
(D). Draw a line passing through points K and T.
(E). Place the compass point at B and using the same distance, draw ANOTHER ARC to intersect the first one at T.
(F). The line KT is perpendicular to line MN at K.
Q. Arrange the steps marked (i) to (v) in CORRECT order while constructing a line parallel to a given line, through a point not on the line using ruler and compasses only.
Step 1. Take a line 'I' and a point 'A' outside 'l'.
Step 2. Take any point B on I and join B to A.
(i) Now with A as centre and the same radius as in previous step, draw an arc EF cutting AB at G.
(ii) With the same opening as in previous step and with G as centre, draw an arc cutting the arc EF at H.
(iii) With B as centre and a convenient radius, draw an arc cutting I at C and BA at D.
(iv) Now, join AH to draw a line 'm'.
Q. To construct a perpendicular to a line (L) from a point (P) outside the line, steps are given in jumbled form.Identify the third step from the following.
1) Draw line PQ.
2)Draw a line L and consider point P outside the line.
3)Take P as a center, draw 2 arcs on line L and name it as points A and B respectively.
4)Taking A and B as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as Q.
Q. What is the 4th step in the construction of ∠PQR, which is equal in measure to ∠ABC ?
1)Draw ray QR.
2) Place the compass point at vertex B of ∠ABC
and taking a convenient distance, draw an arc
to cut the rays BA and BC at points D and E
respectively.

3) Using the same distance again, place the
compass point at point Q of ray QR and draw
an arc. Let this arc cut the ray QR at T.
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